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Topographic modifications to bottom Ekman layer structure

Isaiah Cuadras, James C. McWilliams, and Marcelo Chamecki

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Phys. Rev. Fluids 10, 053802 – Published 19 May, 2025

DOI: https://doi.org/10.1103/PhysRevFluids.10.053802

Abstract

A bottom Ekman layer is defined by a dynamic balance between the Coriolis force, pressure gradient force, and turbulent transport. We investigate how this balance is modified by bottom topography by analyzing Large Eddy Simulations of separating flow over a two-dimensional ridge. The focus is on two cases that include rotation: one where the exterior flow is driven across the ridge (Cross-Hill with Rotation: “CHR”), and another where the flow is driven along the ridge axis (Along-Hill with Rotation: “AHR”). In both cases, the bottom portion of the boundary layer is dominated by topographic disturbances, including a speedup over the hill and a recirculation in the wake. While these near-bottom modifications are rooted in nonrotating flow dynamics (evidenced in nonrotating simulations presented here), they are impacted by the Coriolis force, leading to a wake jet in the along-ridge flow component of CHR and a wake deficit in the along-ridge component of AHR. These features drive magnifications in the ageostrophic transport that cannot be predicted by the bottom stress. Analysis of the transport budget suggests the wake dynamics are sensitive to the strength of the horizontal divergence of the Reynold's stresses, being stronger in CHR than in AHR. This leads to a large nonlocal influence in CHR, where averaging the ageostrophic transport over a distance that is 3 times the hill's total length leads to a more than 30% increase in magnitude when compared to the flat case. Averaging over the same distance in AHR shows negligible differences to the bulk transport relative to the flat case, as the wake is more confined to the topography vicinity. These results show that the influence of rotation on the speedup and recirculation play an essential role in facilitating topographically induced changes to the bulk transport, with an evident dependence on the strength of flow separation.

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References (51)

  1. V. W. Ekman, On the influence of the earth's rotation on ocean-currents, Ark. Mat. Astron. Fys. 2, 1 (1905).
  2. J. Deardorff, A three-dimensional numerical investigation of the idealized planetary boundary layer, Geophys. Fluid Dyn. 1, 377 (1970).
  3. G. N. Coleman, J. H. Ferziger, and P. R. Spalart, A numerical study of the turbulent Ekman layer, J. Fluid Mech. 213, 313 (1990).
  4. E. Deusebio, G. Brethouwer, P. Schlatter, and E. Lindborg, A numerical study of the unstratified and stratified Ekman layer, J. Fluid Mech. 755, 672 (2014).
  5. R. G. Williams and M. J. Follows, The Ekman transfer of nutrients and maintenance of new production over the North Atlantic, Deep Sea Res. Part I 45, 461 (1998).
  6. J. Yang, The seasonal variability of the arctic ocean Ekman transport and its role in the mixed layer heat and salt fluxes, J. Clim. 19, 5366 (2006).
  7. B. Chen, D. Yang, C. Meneveau, and M. Chamecki, Numerical study of the effects of chemical dispersant on oil transport from an idealized underwater blowout, Phys. Rev. Fluids 3, 083801 (2018).
  8. Y. Yoshikawa, T. Endoh, T. Matsuno, T. Wagawa, E. Tsutsumi, H. Yoshimura, and Y. Morii, Turbulent bottom Ekman boundary layer measured over a continental shelf, Geophys. Res. Lett. 37, L15605 (2010).
  9. A. Perlin, J. N. Moum, J. M. Klymak, M. D. Levine, T. Boyd, and P. M. Kosro, Organization of stratification, turbulence, and veering in bottom Ekman layers, J. Geophys. Res.: Oceans 112, C05S90 (2007).
  10. J. R. Taylor and S. Sarkar, Stratification effects in a bottom Ekman layer, J. Phys. Oceanogr. 38, 2535 (2008).
  11. A. Schaeffer, M. Roughan, and J. E. Wood, Observed bottom boundary layer transport and uplift on the continental shelf adjacent to a western boundary current, J. Geophys. Res.: Oceans 119, 4922 (2014).
  12. A. Schaeffer, M. Roughan, and B. D. Morris, Cross-shelf dynamics in a Western Boundary Current regime: Implications for upwelling, J. Phys. Oceanogr. 43, 1042 (2013).
  13. N. Malan, M. Roughan, G. J. Stanley, R. Holmes, and J. Li, Quantifying cross-shelf transport in the east Australian Current System: A budget-based approach, J. Phys. Oceanogr. 52, 2555 (2022).
  14. P. S. Jackson and J. C. R. Hunt, Turbulent wind flow over a low hill, Q. J. R. Meteorol. Soc. 101, 929 (1975).
  15. J. C. R. Hunt, S. Leibovich, and K. J. Richards, Turbulent shear flows over low hills, Q. J. R. Meteorol. Soc. 114, 1435 (1988).
  16. F. T. Smith, P. W. M. Brighton, P. S. Jackson, and J. C. R. Hunt, On boundary-layer flow past two-dimensional obstacles, J. Fluid Mech. 113, 123 (1981).
  17. A. A. S. Pirooz and R. G. J. Flay, Comparison of speed-up over hills derived from wind-tunnel experiments, wind-loading standards, and numerical modelling, Boundary Layer Meteorol. 168, 213 (2018).
  18. A. J. Bowen, The prediction of mean wind speed above simple 2D hill shapes, J. Wind Eng. Ind. Aerodyn. 15, 259 (1983).
  19. F. Hewer, Non-linear numerical model predictions of flow over an isolated hill of moderate slope, Boundary Layer Meteorol. 87, 381 (1998).
  20. R. L. Simpson, J. H. Strickland, and P. W. Barr, Features of a separating turbulent boundary layer in the vicinity of separation, J. Fluid Mech. 79, 553 (1977).
  21. P. R. Spalart and J. H. Watmuff, Experimental and numerical study of a turbulent boundary layer with pressure gradients, J. Fluid Mech. 249, 337 (1993).
  22. Y. Na and P. Moin, Direct numerical simulation of a separated turbulent boundary layer, J. Fluid Mech. 374, 379 (1998).
  23. Z. Yang and P. R. Voke, Large-eddy simulation of boundary-layer separation and transition at a change of surface curvature, J. Fluid Mech. 439, 305 (2001).
  24. N. Wood, The onset of separation in neutral, turbulent flow over hills, Boundary Layer Meteorol. 76, 137 (1995).
  25. S. Cao and T. Tamura, Experimental study on roughness effects on turbulent boundary layer flow over a two-dimensional steep hill, J. Wind Eng. Ind. Aerodyn. 94, 1 (2006).
  26. G. P. Almeida, D. F. G. Durao, and M. V. Heitor, Wake flows behind two-dimensional model hills, Exp. Therm. Fluid Sci. 7, 87 (1993).
  27. H. Ólafsson and P. Bougeault, The effect of rotation and surface friction on orographic drag, J. Atmos. Sci. 54, 193 (1997).
  28. H. Wells, S. Webster, and A. Brown, The effect of rotation on the pressure drag force produced by flow around long mountain ridges, Q. J. R. Meteorol. Soc. 131, 1321 (2005).
  29. H. A. Khaledi, M. Barri, and H. I. Andersson, On the stabilizing effect of the Coriolis force on the turbulent wake of a normal flat plate, Phys. Fluids 21, 095104 (2009).
  30. M. Barri and H. I. Andersson, Turbulent flow over a backward-facing step. Part 1. Effects of anti-cyclonic system rotation, J. Fluid Mech. 665, 382 (2010).
  31. S. Frei, E. Burman, and E. Johnson, Attached and separated rotating flow over a finite height ridge, Phys. Rev. Fluids 9, 084801 (2024).
  32. M. Abkar and F. Porté-Agel, Influence of the Coriolis force on the structure and evolution of wind turbine wakes, Phys. Rev. Fluids 1, 063701 (2016).
  33. T. Zhou and T. Ishihara, Numerical investigation of neutral atmospheric boundary layer flows over flat terrain and three-dimensional hills considering the effects of Coriolis force, J. Wind Eng. Ind. Aerodyn. 240, 105482 (2023).
  34. E. Bou-Zeid, C. Meneveau, and M. Parlange, A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows, Phys. Fluids 17, 025105 (2005).
  35. R. Mittal and G. Iaccarino, Immersed boundary method, Annu. Rev. Fluid Mech. 37, 239 (2005).
  36. B. Chen and M. Chamecki, Turbulent kinetic energy budgets over gentle topography covered by forests, J. Atmos. Sci. 80, 91 (2023).
  37. B. Fornberg, A Practical Guide to Pseudospectral Methods 1 (Cambridge University Press, Cambridge, UK, 1998).
  38. Q. Li, E. Bou-Zeid, and W. Anderson, The impact and treatment of the Gibbs phenomenon in immersed boundary method simulations of momentum and scalar transport, J. Comput. Phys. 310, 237 (2016).
  39. M. Heisel, B. Chen, J. F. Kok, and M. Chamecki, Gentle topography increases vertical transport of coarse dust by orders of magnitude, J. Geophys. Res.: Atmos. 126, e2021JD034564 (2021).
  40. J. Fröhlich, C. P. Mellen, W. Rodi, L. Temmerman, and M. A. Leschziner, Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions, J. Fluid Mech. 526, 19 (2005).
  41. F. Feddersen, E. L. Gallagher, R. T. Guza, and S. Elgar, The drag coefficient, bottom roughness, and wave-breaking in the nearshore, Coastal Eng. 48, 189 (2003).
  42. S. S. Zilitinkevich, On the determination of the height of the Ekman boundary layer, Boundary Layer Meteorol. 3, 141 (1972).
  43. P. K. Kundu, I. M. Cohen, and D. R. Dowling, Fluid Mechanics (Academic, New York, 2015).
  44. R. J. Stevens, J. Graham, and C. Meneveau, A concurrent precursor inflow method for Large Eddy Simulations and applications to finite length wind farms, Renewable Energy 68, 46 (2014).
  45. W. Anderson, J. M. Barros, K. T. Christensen, and A. Awasthi, Numerical and experimental study of mechanisms responsible for turbulent secondary flows in boundary layer flows over spanwise heterogeneous roughness, J. Fluid Mech. 768, 316 (2015).
  46. H. G. Hwang and J. H. Lee, Secondary flows in turbulent boundary layers over longitudinal surface roughness, Phys. Rev. Fluids 3, 014608 (2018).
  47. A. K. Blackadar, Boundary layer wind maxima and their significance for the growth of nocturnal inversions, Bull. Am. Meteorol. Soc. 38, 283 (1957).
  48. B. J. H. V. d. Wiel, A. F. Moene, G. J. Steeneveld, P. Baas, F. C. Bosveld, and A. A. M. Holtslag, A conceptual view on inertial oscillations and nocturnal low-level jets, J. Atmos. Sci. 67, 2679 (2010).
  49. A. Shapiro, E. Fedorovich, and S. Rahimi, A unified theory for the great plains nocturnal low-level jet, J. Atmos. Sci. 73, 3037 (2016).
  50. S. Cao, T. Wang, Y. Ge, and Y. Tamura, Numerical study on turbulent boundary layers over two-dimensional hills — Effects of surface roughness and slope, J. Wind Eng. Ind. Aerodyn. 104–106, 342 (2012), in 13th International Conference on Wind Engineering.
  51. Z. Liu, J. Cao, B. Yan, Y. Wang, and H. Wang, Study of wind-direction effects on flow fields over two-dimensional hills using Large Eddy Simulations, J. Wind Eng. Ind. Aerodyn. 204, 104285 (2020).

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Phys. Rev. Fluids 10, 053802– Published 19 May, 2025
  • Received 26 November 2024
  • Accepted 22 April 2025
Article part of CHORUS
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